http://repub.eur.nl/res/aut/553/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/21017/ 2010-09-01T00:00:00Z We analyse the impact of the Engle and Granger (1987) article by means of its citations over time, and find evidence of a second life starting in the new millennium. Next, we propose a possible explanation of the success of this citation classic. We argue that the conditions for its success were just right at the time of its appearance, because of the growing emphasis on time series properties in econometric modelling, the empirical importance of stochastic trends, the availability of sufficiently long macroeconomic time series, and the availability of personal computers and econometric software for carrying out the new techniques. http://repub.eur.nl/res/pub/21220/ 2010-09-01T00:00:00Z http://repub.eur.nl/res/pub/11120/ 2007-05-15T00:00:00Z It generally is difficult, if not impossible, to fully understand and interpret nonlinear time series models by considering the estimated values of the model parameters only. To shed light on the characteristics and implications of a nonlinear model it can then be useful to consider the effects of shocks on the future patterns of the time series variable. Most interest in such impulse response analysis has concentrated on measuring the persistence of shocks, or the magnitude of their (ultimate) effect. A framework is developed and implemented that is useful for measuring the rate at which this final effect is attained, or the rate of absorption of shocks. It is shown that the absorption rate can be used to examine whether the propagation of different types of shocks, such as positive and negative shocks or large and small shocks follows different patterns. The nonlinear floor-and-ceiling model for US output growth is used to illustrate the various concepts. The presence of substantial asymmetries in both persistence and absorption of shocks is documented, with interesting differences arising across magnitudes of shocks and across regimes in the model. Furthermore, it appears that asymmetry became much less pronounced due to a large decline in output volatility in the 1980s. http://repub.eur.nl/res/pub/13349/ 2006-06-01T00:00:00Z We discuss a method to estimate the confidence bounds for average economic growth, which is robust to misspecification of the unit root property of a given time series. We derive asymptotic theory for the consequences of such misspecification. Our empirical method amounts to an implementation of the subsampling procedure advocated in Romano and Wolf (Econometrica, 2001, Vol. 69, p. 1283). Simulation evidence supports the theory and it also indicates the practical relevance of the subsampling method. We use quarterly postwar US industrial production for illustration and we show that non-robust approaches rather lead to different conclusions on average economic growth than our robust approach. http://repub.eur.nl/res/pub/7601/ 2006-03-15T00:00:00Z To examine cross-country diffusion of new products, marketing researchers have to rely on a multivariate product growth model. We put forward such a model, and show that it is a natural extension of the original Bass (1969) model. We contrast our model with currently in use multivariate models and we show that inference is much easier and interpretation is straightforward. In fact, parameter estimation can be done using standard commercially available software. We illustrate the benefits of our model relative to other models in simulation experiments. An application to a three-country CD sales series shows the merits of our model in practice. http://repub.eur.nl/res/pub/13344/ 2005-07-01T00:00:00Z The parsimonious Bass diffusion model is frequently used to forecast adoptions of new products and to compare the life cycles of specific products across countries. To meet these goals, reliable parameter estimates are needed. We develop the asymptotic theory for the three key parameters in the Bass model. For this purpose, we need to make assumptions about the stochastic error process. On doing so, we arrive at an alternative version of the Bass model than the one usually considered in practice, because our model includes an additional variable and it incorporates heteroscedastic errors. The asymptotic theory entails that the parameters, on standardization by their standard errors, do not have the conventional asymptotic behavior. For practical purposes, it means that the t-statistics do not have an (approximate) t-distribution. Using simulation experiments, we address the issue of how these findings carry over to practical situations. In a next set of simulation experiments, we compare our representation with that of Bass and Srinivasan and Mason. Among other things, we document that these two approaches seriously overestimate the precision of the parameter estimators, and that some parameters suffer from a substantial bias. An analysis of 12 series concerning compact disc penetration supports these simulation results. We see the same type of bias in parameter estimates, and our model delivers more accurate forecasts. http://repub.eur.nl/res/pub/216/ 2002-07-30T00:00:00Z We propose a new empirical representation of the Bass diffusion model, in order to estimate the three key parameters, concerning innovation, imitation and maturity. The representation is based on the notion that the observed data may temporarily deviate from the mean path determined by the underlying hazard rate. Additionally, it rests on the idea that uncertainty about the cumulative process should be smaller, the closer it is to the start of the process and to the level of maturity. Taking this into account, we arrive at an extension of the basic representation proposed in Bass (1969), with an additional heteroskedastic error term. The type of heteroskedasticity can be set by the modeler, as long as it obeys certain properties. Next, we discuss the asymptotic theory for this new empirical model, that is, we focus on the properties of the estimators of the various parameters. We show that the parameters, upon standardization by their standard errors, do not have the conventional asymptotic behavior. For practical purposes, it means that the t-statistics do not have an (approximate) t-distribution. Using simulation experiments, we address the issue how these findings carry over to practical situations. In a next set of simulation experiments, we compare the new representation with that of Bass (1969) and Srinivasan and Mason (1986). We document that these last two approaches often seriously overestimate the precision of the parameter estimators. We also shed light on the effects of temporal aggregation and on the effects of a serious and persisent deviation between the actual data and their mean. Finally, we consider the various empirical representations for a monthly series on installed ATMs. http://repub.eur.nl/res/pub/588/ 2001-12-31T00:00:00Z We discuss a method to estimate the confidence bounds for average economic growth, which is robust to misspecification of the unit root property of a given time series. We derive asymptotic theory for the consequences of such misspecification. Our empirical method amounts to an implementation of the bootstrapping procedure advocated in Romano and Wolf (2001). Simulation evidence supports the theory and it also indicates the practical relevance of the bootstraping method. We use quarterly post-war US industrial production for illustration and we show that non-robust approaches lead to rather different conclusions on average economic growth than our robust approach. http://repub.eur.nl/res/pub/2185/ 2001-11-01T00:00:00Z A unique characteristic of marketing data sets is the logical consistency requirement in market share models that market shares are bounded by 0 and 1, and they sum to unity. To take account of this logical consistency requirement, we propose to test for unit roots in individual market share series within the context of a market share attraction (MCI) framework. Our paper offers new contributions in testing for unit roots in market shares. First, a novel feature of our paper is that we propose a new unit root testing methodology designed to deal with the logical consistency requirement in market share models within the context of a market share attraction (MCI) framework. A second novel component of our paper is that we demonstrate how one could use the Johansen (1995) test to identify unit roots. This is implemented using Eviews software. The Johansen test is a system-based test rather than a single equation test; it is more appropriate given the dependencies in the market share relationships. Finally, we demonstrate using simulations that our procedure works well and improves substantially on the univariate Dickey-Fuller procedure. Accordingly, our procedure leads to better unit root inference than the univariate Dickey-Fuller method; the latter is not that reliable when dealing with market shares. We conclude the paper with suggestions for future research. http://repub.eur.nl/res/pub/6832/ 2001-01-01T00:00:00Z This paper puts forward a method to estimate average economic growth, and its associated confidence bounds, which does not require a formal decision on potential unit root properties. The method is based on the analysis of either difference-stationary or trend-stationary time series models, implementing the robust bootstrapping procedure advocated in Romano and Wolf (2001). Simulation evidence indicates the practical relevance of the method. It is illustrated on quarterly post-war US industrial production. http://repub.eur.nl/res/pub/1637/ 2000-01-20T00:00:00Z A key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to fully understand the structure of the model by considering the estimated values of the model parameters only. Put differently, it often is difficult to interpret a specific nonlinear model. To shed light on the characteristics of a nonlinear model it can then be useful to consider the effect of shocks on the future patterns of a time series variable. Most interest in such impulse response analysis has concentrated on measuring the persistence of shocks, or the magnitude of the (ultimate) effect of shocks. Interestingly, far less attention has been given to measuring the speed at which this final effect is attained, that is, how fast shocks are 'absorbed' by a time series. In this paper we develop and implement a framework that can be used to assess the absorption rate of shocks in nonlinear models. The current-depth-of-recession model of Beaudry and Koop (1993), the floor-and-ceiling model of Pesaran and Potter (1997) and a multivariate STAR model are used to illustrate the various concepts. http://repub.eur.nl/res/pub/2064/ 1997-01-01T00:00:00Z In this paper we propose a model selection strategy for a univariate periodic autoregressive time series which involves tests for one or more unit roots and for parameter restrictions corresponding to seasonal unit roots and multiple unit roots at the zero frequency. Examples of models that are considered are variants of the seasonal unit roots model and the periodic integration model. We show that the asymptotic distributions of various test statistics are the same as well-known distributions which are already tabulated. We apply our strategy to three empirical series to illustrate its ease of use. We find that evidence for seasonal unit roots based on nonperiodic models disappears when periodic representations are considered. http://repub.eur.nl/res/pub/2063/ 1996-10-30T00:00:00Z A periodically integrated autoregressive process for a time series which is observed S times per year assumes the presence of S - 1 cointegration relations between the annual series containing the seasonal observations, with the additional feature that these relations are different across the seasons. This means that there is a single unit root in the vector autoregression for these annual series. In this paper it is shown that temporally aggregating such a process does not affect the presence of this unit root, i.e. the aggregated series is also periodically integrated. http://repub.eur.nl/res/pub/2062/ 1996-01-01T00:00:00Z Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model. http://repub.eur.nl/res/pub/2061/ 1995-01-01T00:00:00Z This paper considers a new approach to the analysis of stable relationships between nonstationary seasonal time series. The basis of this approach is an error correction model in which both long-run effects and adjustment parameters are allowed to vary per season. First, we discuss theoretical arguments for such a periodic error correction model. We define periodic cointegration and compare this to the concept of seasonal cointegration. Next, we analyze statistical inference in the periodic error correction model A sequential procedure is proposed, consisting of a test for periodic cointegration, an estimator of the cointegration parameters and adjustment coefficients, and a class of tests for the hypothesis that some of the parameters are constant over the seasons. The finite sample behavior of the proposed test statistics is analyzed in a limited Monte Carlo exercise. We conclude the paper with an application to a model of aggregate Swedish consumption. http://repub.eur.nl/res/pub/2084/ 1995-01-01T00:00:00Z A periodic autoregressive time-series model assumes that the autoregressive parameters vary with the season. This model can also be represented by a multivariate model for the annual vector containing the seasonal observations. When this multivariate model contains one unit root, a time-series is said to be periodically integrated of order 1. In this paper we propose tests for such a single unit root. These tests for periodic integration are applied to a periodic model for the quarterly German consumption series. http://repub.eur.nl/res/pub/2115/ 1993-01-01T00:00:00Z http://repub.eur.nl/res/pub/2070/ 1992-01-01T00:00:00Z The article discusses the use of some Monte Carlo experiments to investigate the effects of dynamic specification on the size and power of three cointegration tests. The first test, proposed by Engle and Granger (1987), is the residual augmented Dickey-Fuller unit root test. The second is a Wald test for the significance of the error correction mechanism in an autoregressive-distributed lag model, suggested by Boswijk (1989) and further developed in Boswijk (1991). The third test is a likelihood ratio test in a vector autoregressive model, proposed by Johansen (1988) and extended in Johansen and Juselius (1990).